Fuzzy Objective Research Articles

Cost-effectiveness analysis of the mobile phone manufacturing sector by using a novel fuzzy multi-objective programming model

This work presents a novel fuzzy multi-objective programming (FMOP) model with a modified S-curve membership function capable of solving integrated multi-component, multi-supplier, and multi-time-period production planning problems by using fuzzy objectives for the mobile phone manufacturing sector. The proposed model attempts to minimize total manufacturing, total inventory holding and total penalty costs simultaneously in relation to manufacturer/supplier capacity and warehouse space. Additionally, the proposed model provides a systematic means of facilitating the fuzzy decision-making process, enabling decision makers to interactively adjust the search direction during the solution procedure in order to obtain the preferred satisfactory solution of a decision maker (DM). Moreover, adequacy of the proposed model is demonstrated, based on an implementation design involving several scenarios of manufacturing production system for mobile phones. Analytical results provide a valuable reference for decision managers attempting to more thoroughly understand the systematic analysis and potential of cost-effective production planning.

Hybridizations of genetic algorithms and neighborhood search metaheuristics for fuzzy bus terminal location problems

We propose modified hybridizations of genetic algorithms with some neighborhood search based metaheuristics. In our hybrid algorithms, we consider gradually increasing probability for the application of the neighborhood search procedure on the best individuals as the number of iterations of the genetic algorithm increases. We implement the proposed hybrid algorithms and compare their performance with two other recently proposed hybrid algorithms which, in contrast, use the neighborhood search procedure on all the individuals of the population, two hybrid algorithms applying simulated annealing on the best individual in the papulation in every iteration and three non-hybrid metaheuristic algorithms. To investigate the effectiveness of the proposed algorithms, we apply the algorithms to our proposed fuzzy bus terminal location problem models. The fuzzy model is considered to have fuzzy number of passengers corresponding to the nodes as well as fuzzy neighborhoods, together with preassigned lower and upper bounds for the number of required terminals. The algorithms are tested on a variety of randomly generated large scale fuzzy bus terminal location problems in with fuzzy cost coefficients. The fuzzy objective is transformed into a crisp one by use of a ranking function. The computational experiments demonstrate the effectiveness of the proposed algorithms on large scale problems. Finally, to show the effectiveness of our proposed hybridizations, we also make a comparative study of our algorithms on crisp facility location and quadratic assignment test problems.

Method for Optimizing the Dual of Linear Fuzzy Programming Problems

This article’s goal is to support the existence of the dual in a Linear Fuzzy Real environment and focus on its application to Linear fuzzy program problems. This concept will apply to linear fuzzy programming problems that contain fuzzy constraints with a crisp objective function, crisp constraints with a fuzzy objective function, or fuzzy constraints with a fuzzy objective function. It is also proposed here that optimizing fuzzy constraints and objectives of the dual linear program that consist of a triplet and are much like triangular fuzzy numbers, but differ in that they are a hybrid fuzzy number that contains characteristics that are both fuzzy and crisp.

Cell loading and manpower allocation with fuzzy multiple objectives in synchronised manufacturing cells

Cell loading and manpower allocation with fuzzy multiple objectives in synchronised manufacturing cells

Analysis of FM/FM/c queuing system: using fuzzy approach and parametric nonlinear programming

Applying fuzzy principles and approaches to the queue systems will provide more extensive and realistic applications of them. A queue system of M/M/c is studied based on fuzzy approach in this paper. This system was proposed as a FM/FM/c system with probability of the presence of customers in the system and utility factor. In addition, performance measurement was developed using the concept of parametric nonlinear programming and characteristics of fuzzy numbers. For further analysis, a FM/FM/c queuing system was considered to determine most appropriate value for the number of servers by using the concept of fuzzy relations and inference and fuzzy multiple objective decision making. The results of this research show that we can determine appropriate number of servers and we can do it perfectly and actually analyse based on system situations and management preferences.

Cell loading and manpower allocation with fuzzy multiple objectives in synchronised manufacturing cells

This paper seeks to determine the feasibility of using fuzzy concepts in cell loading and manpower allocation to solve multiple objectives scheduling problems in a cellular manufacturing environment. Various manpower allocation levels were considered and then products were assigned to the cells and followed up by product sequencing and manpower allocation decisions in each cell by considering the fuzzy concept. The number of operators needed in a time bucket may be different based on the manpower requirement for each process. Fuzzy mathematical model for cell loading and cell sequencing were developed in multiple cells with multiple objectives. The objectives were to minimise the total manpower shortages simultaneously with the minimum number of time buckets with manpower allocation shortage. Then, additional manpower as floaters were considered to reduce the total number of manpower shortages. The results revealed that multiple objectives with fuzzy functions balanced the manpower allocation and minimised the total shortage.

A Mathematical Model for Fuzzyp-Median Problem with Fuzzy Weights and Variables

We investigate thep-median problem with fuzzy variables and weights of vertices. The fuzzy equalities and inequalities transform to crisp cases by using some technique used in fuzzy linear programming. We show that the fuzzy objective function also can be replaced by crisp functions. Therefore an auxiliary linear programming model is obtained for the fuzzyp-median problem. The results are compared with two previously proposed methods.

A New Bi-Objective Location-Routing-Inventory Problem with Fuzzy Demands

This paper presents a new bi-objective location-routing-inventory (LRI) problem that considers a multi-period and multi-product problem with heterogeneous fleets in a two-echelon distribution network. The uncertainty in the demand of customers is defined by a fuzzy approach. Two conflicting fuzzy objective functions are included, first of which is to minimize the costs of the used vehicles, fuel consumption, inventory holding, transporting and locating open distribution centers. The second objective is to minimize the shortage of products for each customer. Numerical results demonstrate the validity of the presented model and show the ability of the model to confront real cases.

FCM Clustering Algorithms for Segmentation of Brain MR Images

The study of brain disorders requires accurate tissue segmentation of magnetic resonance (MR) brain images which is very important for detecting tumors, edema, and necrotic tissues. Segmentation of brain images, especially into three main tissue types: Cerebrospinal Fluid (CSF), Gray Matter (GM), and White Matter (WM), has important role in computer aided neurosurgery and diagnosis. Brain images mostly contain noise, intensity inhomogeneity, and weak boundaries. Therefore, accurate segmentation of brain images is still a challenging area of research. This paper presents a review of fuzzyc-means (FCM) clustering algorithms for the segmentation of brain MR images. The review covers the detailed analysis of FCM based algorithms with intensity inhomogeneity correction and noise robustness. Different methods for the modification of standard fuzzy objective function with updating of membership and cluster centroid are also discussed.

Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solution of the problem, we apply deviation degree measures to deal with the fuzzy constraints and use a ranking function method of fuzzy numbers to rank the upper and lower level fuzzy objective functions. Then the fully fuzzy bilevel linear programming problem can be transformed into a deterministic bilevel programming problem. Considering the overall balance between improving objective function values and decreasing allowed deviation degrees, the computational procedure for finding a fuzzy optimal solution is proposed. Finally, a numerical example is provided to illustrate the proposed approach. The results indicate that the proposed approach gives a better optimal solution in comparison with the existing method.

Parameter Modification Guiding Optimization Design and Tests of a Rotary Transplanting Mechanism for Rice Plug Seedlings

A parameter modification guiding optimization method combined with fuzzy optimization was applied to improve the design of a rice plug seedling transplanting mechanism using a planetary gear train with elliptical gears and an incomplete non-circular gear. The laboratory kinematics was examined, and seedling transplanting tests were conducted. Based on the work principle analysis of the transplanting mechanism for rice plug seedlings, numerical kinematic objective functions were established using fuzzy objectives requirements such as transplanting trajectory and posture. Subordinate functions were determined to describe the objective functions. Then the optimization model of the mechanism was constructed which took the value of the subordinate degree of objective functions as the optimization objectives and the motion interference, height of the transplanting trajectory and mechanical structure as the constraint conditions. Parameter guiding optimization software based on Visual Basic 6.0 was developed independently to determine a set of better parameters for the mechanism, which can reduce dependence on expert experience and improve the efficiency of the design. The mechanism structure was designed, and a physical prototype was manufactured. A high-speed digital video camera and image processing technology were used to perform the kinematics bench tests to obtain the transplanting trajectory and posture of the mechanism. The consistency between the test results and theoretical results shows that the optimized mechanism can satisfy the transplanting requirements and that the design method and results are also accurate. Finally, rice seedling transplanting tests were conducted to verify the transplanting performance of the mechanism. The mechanism extracted 200 seedlings per minute per row with a success ratio of 95.89%; the mechanism also displayed a good effect in seedling pushing, showing that the mechanism could be applied in a practical machine.

Multi-item Supplier Selection Model with Fuzzy Risk Analysis Studied by Possibility and Necessity Constraints

Three different supplier selection models have been developed in crisp and fuzzy environments. Here two objective functions have been considered, profit and risk. In this paper, profit has been maximized and risk has been minimized with some constraints. Each supplier has an limited capacity. The purchasing cost of each item from different supplier as well as associative risk is known. The total space and budget of a retailer are constant. In Model I, all the parameters are considered as crisp. In Model II, the demand has been considered as fuzzy. In Model III, the risk values and demand have been considered as fuzzy. To defuzzyfy the fuzzy constraints, necessity and possibility have been introduced. To defuzzyfy the fuzzy objective, two different methods, credibility measure and α-cut method have been introduced. All the models have been illustrated numerically using multi-objective genetic algorithm (MOGA). Also a sensitivity analysis has been done taking different sets of risk values and a comparison result has been shown for credibility measure and α-cut method for Model III.

An Interval Approximation Approach for a Multiobjective Programming Model with Fuzzy Objective Functions

Research in optimization under uncertainty is alive. It assumes different shapes and forms, all concurring to the general goal of designing effective and efficient tools for handling imprecision in an Optimization setting. In this paper we present a new approach for dealing with multiobjective programming problems with fuzzy objective functions. Similar to many approaches in the literature, our approach relies on the deffuzification of involved fuzzy quantities. Our improvement stem from the choice of a deffuzification operator that captures essential features of fuzzy parameters at hand rather than those that yield single values, leading to a loss of many useful information. Two oracles play a pivotal role in the proposed method. The first one returns a near interval approximation to a given fuzzy number. The other one delivers a Pareto Optimal solution of the resulting multiobjective program with interval coefficient. A numerical example is also provided for the sake of illustration.

Stochastic facility and transfer point covering problem with a soft capacity constraint

Existing models for transfer point location problems (TPLPs) do not guarantee the desired service time to customers. In this paper, a facility and TPLP is formulated based on a given service time that is targeted by a decision maker. Similar to real-world situations, transportation times and costs are assumed to be random. In general, facilities are capacitated. However, in emergency services, they are not allowed to reject the customers for out of capacity reasons. Therefore, a soft capacity constraint for the facilities and a second objective to minimize the overtime in the facility with highest assigned demand are proposed. To solve the biobjective model with random variables, a variance minimization technique and chance-constraint programming are applied. Thereafter, using fuzzy multiple objective linear programming, the proposed biobjective model is converted to a single objective. Computational results on 30 randomly designed experimental problems confirm satisfactory performance of the proposed model in reducing the variance of solutions as well as the overtime in the busiest facility.

Robust fuzzy clustering using nonsymmetric student׳s t finite mixture model for MR image segmentation

Accurate tissue segmentation from magnetic resonance (MR) images is an essential step in clinical practice. In this paper, we introduce a robust fuzzy clustering scheme for finite mixture model fitting, which exploits the merits of the mixture of the nonsymmetric Student׳s t-distribution and mean template to reduce the sensitivity of the segmentation results with respect to noise. This approach utilizes a fuzzy objective function regularized by the Kullback–Leibler (KL) divergence term and sets the dissimilarity function as the negative log-likelihood of the nonsymmetric Student׳s t-distribution and mean template. The advantage of this fuzzy clustering scheme is that the spatial relationships among neighbouring pixels are taken into account with the help of the mean template so that the proposed method is more robust to noise than several other existing fuzzy c-means (FCM)-based algorithms. Another advantage is that the application of the nonsymmetric Student׳s t-distribution mixture model allows the proposed model to fit different shapes of observed data. Experiments using synthetic and real MR images show that the proposed model has considerably better segmentation accuracy and robustness against noise compared with several well-known finite mixture models.

Comprehensive fuzzy multi-objective multi-product multi-site aggregate production planning decisions in a supply chain under uncertainty

The main focus of this paper is to develop a model considering some significant aspects of real-world supply chain production planning approved by industries. To do so, we consider a supply chain (SC) model, which contains multiple suppliers, multiple manufactures and multiple customers. This model is formulated as a fuzzy multi objective mixed-integer nonlinear programming (FMOMINLP) to address a comprehensive multi-site, multi-period and multi-product aggregate production planning (APP) problem under uncertainty. Four conflicting objectives are considered in the presented model simultaneously, which are (i) to minimize the total cost of the SC (production costs, workforce wage, hiring/firing and training costs, transportation cost, inventory holding cost, raw material purchasing cost, and shortage cost), (ii) to improve customer satisfaction, (iii) to minimize the fluctuations in the rate of changes of workforce, and (iv) to maximize the total value of purchasing in order to consider the impact of qualitative performance criteria. This model is converted to multi-objective mixed-integer linear programming (MOMILP) through three steps of the developed method and then the MOMILP model is solved by two different methods. Additionally, comparison of these two methods is presented and the results are analyzed. Finally, the efficiency of the model is investigated by a real industry SC case study.

Electricity monitoring system with fuzzy multi-objective linear programming integrated in carbon footprint labeling system for manufacturing decision making

In the novel electricity monitoring system designed in this study, manufacturing data with energy consumption are transformed in real time in the communication module and analysis module and then sent to such information devices as notebooks, i-Pads, or i-Phones. A fuzzy multiple objective linear programming (FMOLP) model is formulated to integrate the designed system for making decision associated with about environmental regulations and cost-effectiveness of carbon emissions in manufacturing firms given a carbon footprint label (CFL). Implementation results demonstrate that the proposed system is very effective in terms of CFL, cost-effectiveness, and manufacturing capacity. Importantly, the electric monitoring system can be practically installed in specific equipment to acquire electric consumption in real time and then helped decision makers to achieve a satisfactory solution in which manufacturing costs and CFL are simultaneously considered under restrain of electricity uncertainty.

An inexact multi-objective programming model for water resources management in industrial parks of Binhai New Area, China.

In recent years, Binhai New Area of Tianjin has been suffering severe water shortage due to climate change and industrial activities. Integrated and effective water resources management approaches are urgent for the sustainable development of industrial parks in Binhai New Area. However, uncertainties exist in many aspects of the water resources system and are inevitably problematic for water resources planning and policy-making. To address these uncertainties, an interval multiple-objective programming model was developed here to support the long-term planning of industrial water resources management in Binhai New Area, Tianjin, China. The model incorporated both multiple-objective programming and interval linear programming into a general programming framework. The developed model could handle the uncertainties and complexities of the water management system, and also allowed decision makers to adjust fuzzy objective control decision variables to satisfy multiple holistic and interactive objectives. The solutions are useful for planning adjustments of the existing water allocation patterns in Binhai New Area.

Fractional transportation problem with fuzzy parameters

The fractional transportation problem (FTP) plays an important role in logistics and supply management for reducing cost and improving service. In the real world, however, the parameters in the models are seldom known exactly and have to be estimated. This paper investigates the FTP where the cost coefficients and right-hand sides are represented by fuzzy parameters. Intuitively, when the parameters in the FTP are fuzzy numbers, the derived objective value should be also a fuzzy number. Based on Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the fuzzy objective value of the FTP with fuzzy parameters. By applying the dual formulation of linear fractional programming and variable substitution techniques, the two-level mathematical programs are transformed into ordinary one-level linear programs to solve. At a specific $$\alpha $$ź-cut, solving the pair of linear programs produces the bounds of the objective value of the fuzzy FTP. By collecting the bounds from different $$\alpha $$ź levels, one can depict the shape of the membership function. An example illustrates how to apply the concept of this paper to solve the fuzzy FTP problem.

A decision model for cost effective design of biomass based green energy supply chains

The core driver of this study is to deal with the design of anaerobic digestion based biomass to energy supply chains in a cost effective manner. In this concern, a decision model is developed. The model is based on fuzzy multi objective decision making in order to simultaneously optimize multiple economic objectives and tackle the inherent uncertainties in the parameters and decision makers’ aspiration levels for the goals. The viability of the decision model is explored with computational experiments on a real-world biomass to energy supply chain and further analyses are performed to observe the effects of different conditions. To this aim, scenario analyses are conducted to investigate the effects of energy crop utilization and operational costs on supply chain structure and performance measures.